They admit freely that one of their core mandates is "price stability", which I'm going to go out on a limb and say includes the price of real-estate not doubling in under a decade..
Well, you're welcome to go out on that particular limb, but it's very rickety and won't support the weight you want it to. "Price stability" in this context simply means low-and-predictable inflation (the usual expressed target is 2% per year). The Fed has no more reason to worry about a sudden spike specificaly in real-estate prices than it does to worry about a sudden doubling of Pringles' prices, except as it affects the overall economy.
(Which I admit real estate is more likely to do than some random snack food.)
But one of the effects, and take-away lessons, of the tech boom in the late 1990s is that growth in one sector of the economy doesn't necessarily mean a bubble or an impending disaster. Greenspan had it right when he let the party run in 1995-97 instead of pulling the interest rate trigger; the rise of the Internet and e-commerce really has made fundamental changes in the global consumer economy, and we're still working out some of the implications. Even factoring in the effects of the tech bust, the US (and world) economy is
awesomely more productive now than it was in 1990, in part because anyone can now sell anything to anyone, which is changing equilibrium prices all over the place. (Video tapes and CDs are now mostly valueless, for example, but data mining algorithms are priceless, precisely because there is more data to mine. Traditional stockbrokers are losing their shirts; on-line trading portals are making mints. Et cetera.)
A more prosaic example is how average cell phone prices shot up when smartphones (and particularly the iPhone) were introduced. The smart phone was so clearly a better product that so clearly met
some people's needs that they were willing to pay high-end PDA prices for a phone. This isn't a sign of price instability, but of a changing market (and a new product on the market that changes the game).
I don't think we've yet figured out where the new equilibrium price is on real estate; I suspect it will end up substantially higher than it was in 1995, precisely because the process of home selling has changed so much. It used to be that if you bought a house, you went to an agent, who showed you a dozen or so houses, and you picked the one you liked best. But he didn't often show you more houses than that, because showing houses was time consuming and expensive.
Now you do most of your own legwork; you can take virtual tours or virtual "open houses" of a hundred houses in a single evening, and then mail the agent for the particulars of your favorite in a much larger set. Each house is being viewed by many more buyers, which means there's a much better chance for a good fit and that you're more likely to find a house that you really want instead of one you will settle for, which in turn means you will be willing to pay more for the house. And because the houses are being viewed by more buyers, the sellers are having to put more work (and cost) into the houses they want to sell. "Curb appeal" is becoming less important than "page appeal" because the web page is where you make your first impression -- and if the house doesn't display well in IE, no one will even bother to do the drive-by and see if they like it.
So, basically, just because house prices are going up in an otherwise relatively stable economic environment doesn't mean that "prices" are unstable.